Stable Complete Intersections

A complete intersection of n polynomials in n indeterminates has only a finite number of zeros. In this paper we address the following question: how do the zeros change when the coefficients of the polynomials are perturbed? In the first part we show how to construct semi-algebraic sets in the parameter space over which all the complete intersection ideals share the same number of isolated real zeros. In the second part we show how to modify the complete intersection and get a new one which generates the same ideal but whose real zeros are more stable with respect to perturbations of the coefficients.Comment: 1 figur

Corrigendum for "Almost vanishing polynomials and an application to the Hough transform"

In this note we correct a technical error occurred in [M. Torrente and M.C. Beltrametti, "Almost vanishing polynomials and an application to the Hough transform", J. Algebra Appl. 13(8), (2014)]. This affects the bounds given in that paper, even though the structure and the logic of all proofs remain fully unchanged.Comment: 30 page

Thinning out redundant empirical data

Given a set $X$ of "empirical" points, whose coordinates are perturbed by errors, we analyze whether it contains redundant information, that is whether some of its elements could be represented by a single equivalent point. If this is the case, the empirical information associated to $X$ could be described by fewer points, chosen in a suitable way. We present two different methods to reduce the cardinality of $X$ which compute a new set of points equivalent to the original one, that is representing the same empirical information. Though our algorithms use some basic notions of Cluster Analysis they are specifically designed for "thinning out" redundant data. We include some experimental results which illustrate the practical effectiveness of our methods.Comment: 14 pages; 3 figure

Stable Border Bases for Ideals of Points

Let $X$ be a set of points whose coordinates are known with limited accuracy; our aim is to give a characterization of the vanishing ideal $I(X)$ independent of the data uncertainty. We present a method to compute a polynomial basis $B$ of $I(X)$ which exhibits structural stability, that is, if $\widetilde X$ is any set of points differing only slightly from $X$, there exists a polynomial set $\widetilde B$ structurally similar to $B$, which is a basis of the perturbed ideal $I(\widetilde X)$.Comment: This is an update version of "Notes on stable Border Bases" and it is submitted to JSC. 16 pages, 0 figure

Feasibility of the tandem reaction of isomerization-telomerization

The aim of this project consists of detennining the feasibility of a new tandem reaction comprising isomerization and telomerization steps starting from internal diolefins. This type of reactions achieves not only a minimization 9fthe number of steps but also potentially reduces waste fonnation and process capital costs, thus fulfilling the main objectives of Green Chemistry towards the design of sustainable processes. Telomerization is a 100% atom efficient route to the fonnation of functionalized long chain molecules. However, only telomerization of tenninal . conjugated dienes has been reported which limits its applications due to the thennodynamically unfavourable presence of tenninal dienes in natural feedstocks. If proved feasible, the proposed tandem reaction would open opportunities for the utilization ofnew feedstocks and a potentially significant industrial impact. Titanate nanotubes was found to be a good support for metal catalysts (Pd, Rh, Ru), showing high activity in the isomerization of diolefins and very high selectivity for the reaction with allylbenzene. A novel Ru-PPh3-resin catalyst was also highly active in diolefins isomerization (including linoleic acid) with similar catalytic activity than homogeneous catalysts and the possibility of being reused without loss of activity. Screening of homogeneous catalysts based on phosphorus and carbene ligands was carried out for the telomerization reaction and the influence of different operation conditions such as temperature, initial concentration and the nature of nucleophiles was investigated. Heterogeneous catalysts based on DVBresins were also studied, revealing an unusual selectivity to tail-to-head products by Pd-(dvds)-PPh3-resin in the reaction of isoprene with methanol. The telomerization reaction was extended to 1,3-hexadiene when long-chain alcohols are used as nucleophiles and Pd(Imes)(dvds) as catalyst, opening opportunities for long-chain reactants. Finally, the feasibility of tandem reactions was successfully demonstrated with the best results obtained with homogeneous isomerization and telomerization catalysts in the presence of free carbene ligands in the reaction medium.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Not citizens, Not Real People. The Italian Way of Governing Immigration through the Criminal Justice System

The aim of this article is to describe the specious use made of the Italian criminal justice system as a device to manage the demands for security due to the general perception of increased immigration flows in Italy. In particular, the article analyses - in each stage of the penal system from substantive criminal law, through criminal procedure law, to the prison system - the connection between the processes of criminalization and the use of extrajudicial measures to control immigration flows (such as border controls and expulsions). The results suggest that this criminal ‘double track’ (Italian citizens on the one side and migrants on the other) - with the subsequent hyper-incarceration of aliens and their final deportation as a consequence of the breach of either or both administrative and criminal law -is a disguised but deliberate choice of recent Italian legislative policy regarding the justice system.El objetivo del presente artículo es describir el uso engañoso que se hace del sistema penal italiano como un dispositivo para gestionar las demandas de seguridad justificadas en la percepción generalizada de aumento de los flujos migratorios en Italia. En particular, el artículo analiza - en cada etapa del sistema penal, derecho penal sustantivo, derecho procesal penal y sistema penitenciario - la conexión entre los procesos de criminalización y el uso de medidas extrajudiciales para controlar los flujos migratorios (como los controles fronterizos y las expulsiones). Los resultados sugieren que esta 'doble vía' penal (ciudadanos italianos por un lado y migrantes por el otro) - con el subsecuente hiperencarcelamiento de extranjeros, así como su deportación final como consecuencia de la vulneración de las leyes administrativas y/o penales - se configura como una elección disfrazada, aunque deliberada de la reciente política legislativa italiana con respecto al sistema de justicia

Proper measures of connectedness

The concept of connectedness has been widely used in financial applications, in particular for systemic risk detection. Despite its popularity, at the state of the art, a rigorous definition of connectedness is still missing. In this paper we propose a general definition of connectedness introducing the notion of proper measures of connectedness (PMCs). Based on the classical concept of mean introduced by Chisini, we define a family of PMCs and prove some useful properties. Further, we investigate whether the most popular measures of connectedness available in the literature are consistent with the proposed theoretical framework. We also compare different measures in terms of forecasting performances on real financial data. The empirical evidence shows the forecasting superiority of the PMCs compared to the measures that do not satisfy the theoretical properties. Moreover, the empirical results support the evidence that the PMCs can be useful to detect in advance financial bubbles, crises, and, in general, for systemic risk detection